DaS: Implementing Dense Ising Machines using Sparse Resistive Networks

Ising machines have generated much excitement in recent years due to their promise for solving hard combinatorial optimization problems. However, achieving physical all-to-all connectivity in IC implementations of large, densely-connected Ising machines remains a key challenge. We present a novel approach, DaS, that uses low-rank decomposition to achieve effectively-dense Ising connectivity using only sparsely interconnected hardware. The innovation consists of two components. First, we use the SVD to find a l o w-rank a p proximation o f t h e I s ing c o upling matrix while maintaining very high accuracy. This decomposition requires substantially fewer nonzeros to represent the dense Ising coupling matrix. Second, we develop a method to translate the low-rank decomposition to a hardware implementation that uses only sparse resistive interconnections. We validate DaS on the MU-MIMO detection problem, important in modern telecommunications. Our results indicate that as problem sizes scale, DaS can achieve dense Ising coupling using only 5%-20% of the resistors needed for brute-force dense connections (which would be physically infeasible in ICs). We also outline a crossbar-style physical layout scheme for realizing sparse resistive networks generated by DaS.